Barca beat Malaga 3-1 in La Liga on Sunday and coach Tito Vilanova and his Malaga counterpart Manuel Pellegrini both rested top players for the cup clash at the Nou Camp.
After withstanding a barrage of early Barca attacks, Malaga drew first blood in the 25th minute when Thiago Alcantara dithered just outside his penalty area. He was dispossessed by Manuel Iturra who slotted past the stranded Jose Manuel Pinto.
Barca's reaction was swift and another defensive lapse gifted them an equaliser three minutes later.
Lionel Messi, who showed off his four FIFA Ballon d'Or awards to the home fans before kick-off, robbed Weligton on the right and sped into the area before curling a low shot beyond Carlos Kameni.
Barca took the lead a minute later when captain Carles Puyol stooped to meet Alcantara's corner and sent a looping header over Kameni and in off a post.
Neither side created much danger in the second half but Malaga looked to be in serious trouble when Ignacio Monreal picked up a straight red card for felling Pedro when he was through on goal with 15 minutes left.
However, Barca failed to make their numerical advantage count and Ignacio Camacho was left unmarked at the far post to clip in a 90th-minute equaliser.
Coming at the end of one of the sloppiest Barca performances of the season, the goal gave Malaga hope for next week's return leg at their Rosaleda stadium on the south coast.
The La Liga leaders should have been out of sight but squandered a number of clear chances, with Chile forward Alexis Sanchez particularly wasteful.
DISAPPOINTING DEBUT
Barca sporting director Andoni Zubizarreta said the tie was "very balanced" after the first leg and praised Malaga for their fighting performance.
"We could have scored the odd goal more in the first half," the former Barca and Spain goalkeeper told television broadcaster Canal Plus.
"What we have to do now is go there with the goal of winning," he added.
Real are the likely opponents in the last four after Jose Mourinho's side beat Valencia 2-0 at the Bernabeu in the first leg on Tuesday.
New Sevilla coach Unai Emery, appointed this week to replace the sacked Michel, had a disappointing debut when the Andalusian club were held to a 0-0 draw at Real Zaragoza.
The winners of the quarter-final tie will meet Atletico Madrid or Real Betis, who play their first leg at Atletico's Calderon stadium on Thursday, in the last four.
